Implementasi Numerik Berbagai Kondisi Batas pada Persamaan Air Dangkal Menggunakan Metode Elemen Hingga Terbaru Konformal dan Non-Konformal - Swastika, Pt Veri; Sulvianuri, Rani; Gautama, I Putu Winada (Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University, 2024)
In this paper, we extend the capability of a newly developed numerical scheme based on our preceding linear conformal and non-conformal finite element methods (FEM) to study 2D shallow water equations (SWE) with various boundaries. Unlike usual approach, we approximate the unknown in a staggered grid due to the use of linear alternating basis. Here, the free surface is approximated using a conformal while the velocity potential is approximated using a non-conformal linear basis. As a result, the varational problem must be reformulated. The resulting scheme is a ODE system which is easy to solve by any time integration method. Therefore, our method is staggered in space, explicit, flexible and simple to implement. The simulation results show that the flexibility of the scheme can be interpreted as the successful use of various boundary conditions. Keywords: 2D SWE, staggered finite element, non-conformal basis, influx boundary